Preheat your oven to 350°F (175°C). Lightly grease a 9x9-inch baking dish or 10-inch cast-iron skillet.

Prepare the filling: In a large bowl, gently toss the peeled and sliced peaches with granulated sugar, lemon juice, cornstarch, vanilla extract, almond extract (if using), and salt until evenly coated. The mixture should look glossy and slightly thickened.

Make the topping: In a medium bowl, combine oats, flour, brown sugar, cinnamon, nutmeg, and salt. Add the cold butter cubes and use your fingers or a pastry cutter to work the butter into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces remaining. Stir in nuts if using.

Pre-cook the filling: For the best fresh peach crisp that's never soggy, pour the peach mixture into your prepared baking dish and bake for 10 minutes on its own. This crucial step helps release and evaporate some of the excess moisture before adding the topping.

Add the topping: Remove the dish from the oven and evenly sprinkle the crisp topping over the pre-baked peaches, covering them completely.

Bake until golden: Return the dish to the oven and bake for 35-40 minutes until the topping is golden brown and the filling is bubbling around the edges.

Cool slightly: Allow the crisp to rest for at least 15 minutes before serving. This cooling period allows the filling to set up properly.